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Über dieses Buch

This book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Mathematical Tools and Preliminary Results

Abstract
We give some fundamental definitions and some Hardy-type inequalities with boundary or interior degeneracy. We also show the equivalence between null controllability and observability inequality.
Genni Fragnelli, Dimitri Mugnai

Chapter 2. The Non Singular Case:

Abstract
We show Carleman estimates for parabolic problems in divergence or non divergence form with degeneracy at the boundary or in the interior of the space domain. By them we obtain observability inequalities, proving that the problems are null controllable.
Genni Fragnelli, Dimitri Mugnai

Chapter 3. A Singular Nondegenerate Parabolic Equation

Abstract
We consider non degenerate singular parabolic problems, giving some existence or non existence results, which depend on the value of the parameter of the singular term. Null controllability results are presented, as well.
Genni Fragnelli, Dimitri Mugnai

Chapter 4. The Case of a Boundary Degenerate/Singular Parabolic Equation

Abstract
We consider parabolic problems in divergence form with boundary degeneracy and power singularity, showing well posedness and null controllability.
Genni Fragnelli, Dimitri Mugnai

Chapter 5. The Case of an Interior Degenerate/Singular Parabolic Equation

Abstract
We consider parabolic problems in divergence and non divergence form with interior degeneracy and singularity given by general functions, showing well posedness and null controllability.
Genni Fragnelli, Dimitri Mugnai

Backmatter

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